Question

If EB is the angle bisector of ∠ABD and BD = BC = 5 cm, find DC.

• A. 5 cm
• B. 8 cm
• C. 4 cm
• D. 12 cm

Answer 1

The correct option is A

5 cm

∠ABD = 2 $\times$ ∠ABE = 2 $\times$ ${60}^{\circ }$ = ${120}^{\circ }$
∠ABD = ∠BCD + ∠BDC (Exterior Angle Property)
Also, BD = BC $\Rightarrow$ ∠BDC = ∠BCD = x (Assumed)
So, x + x = 2x = ${120}^{\circ }$ $\Rightarrow$ x = ${60}^{\circ }$
In ∆BDC, ∠BDC = ∠BCD = ${60}^{\circ }$ $\Rightarrow$ ∠DBC = ${60}^{\circ }$
So, ∆BDC is an equilateral triangle. That means DB = BC = CD = 5 cm.